Physics of Structural Mechanics

Stress analysis is a very important task for engineers in civil, mechanical, aerospace and many other subjects. Although it is called stress analysis, it looks for both stress and strain over the structure so that to determine the condition of a structure under external loads. Stress analysis can be performed through different ways, for example, experimental testing, analytical solution or computational simulation, experimental testing, or a combination of methods or a combination of the methods. In this course, we will start from the objectives and applications of stress analysis and we will address the importance of an engineer’s role in computational simulation of stress analysis.

In engineering, the deformation of a structure is related to the concept of strain. When an external load is applied to an engineering assembly, its components may experience a change in shape, quantified by “strain.” The strain is useful in determining the amount of elongation or distortion a structure may experience under various loading conditions. This course will discuss how strain is measured in experiments and how it is described mathematically in stress analysis. One important takeaway of this course is that the definition of strain is not unique and knowing the difference between them is critical in defining material property and evaluating strain results.

“Mechanics of Materials” is the study of the relationship between the external loads and internal forces experienced by any structure. The magnitude of the internal force at a point in the structure can be quantified as “stress.” In this course, we introduce stress in tensor format first, followed by how and why the stress tensor is transformed to principal stress and equivalent stress. We also discuss the balance of the internal forces, which leads to local equilibrium, which is the basic governing equation in stress analysis. Understanding local equilibrium gives us a good foundation to study the computational simulation of stress analysis.

The dynamic behavior of structures is an important concern across many disciplines of engineering. By understanding structural dynamics, civil engineers can design buildings that can withstand severe dynamic loading from earthquakes and hurricanes, aerospace engineers can control the vibration of aircraft wings under turbulence, and mechanical engineers can design crash protection features to reduce the force of a collision. In this course, we will learn the basic principles and applications of structural dynamics in engineering.

All structures respond to external loads in a nonlinear fashion. However, the nonlinear nature is profound and important in only certain cases. There are several linear and nonlinear solvers that are available to analyze these systems and picking the correct solver is often a choice between computational cost and accuracy. In this Ansys Innovation Course on “Introduction to Nonlinearities” we will present a discussion on what is meant by a structure’s mechanical response and what makes it nonlinear. Upon completion, students will be able to make informed decisions on whether a linear or a nonlinear solver is best suited for analyzing a system.

Every structure undergoes changes over a period; some occur over short time periods while others take a long time. While time is always an independent variable in play, it is not necessary to consider it in analyzing all systems. But how do we identify when time may be ignored (e.g., static and quasi-static analyses) and when is it necessary to be considered? In this Ansys Innovation Course on “Time Domain Analysis,” we will introduce the governing equations of motion and discuss when and how an independent time variable is important in studying a structure’s mechanical response. We will discuss what factors introduce time dependency and when the analysis may be idealized as a static analysis. Students will learn the importance of considering inertial effects in an analysis and how they may change a system’s mechanical behavior.

Solids behave differently when they are subjected to large deformations as opposed to small ones. This is due to the change in their shape and it often introduces a form of nonlinearity known as geometric nonlinearity. The degree to which this nonlinearity affects the solution accuracy is controlled by certain variables, including the nature of the loading, the material used, boundary conditions, etc.; While using small deformation theory to solve for a structure’s response is inexpensive, it may be inaccurate when this nonlinearity is prominent. In this Ansys Innovation Course on “Large Deformations”, we will introduce the physical nature of large deformations and how they are captured mathematically. We will present the simplifying assumptions that are made when we use small deformation theory and the impact they have on the accuracy of a solution using several examples. Completing this course will enable you to answer a simple but very important question: When do we use large deformation theory to analyze a structure’s response?

Modal analysis is the fundamental dynamic analysis type, providing the natural frequencies at which a structure will resonate. These natural frequencies are of paramount importance in various engineering fields. Suspensions are usually tuned to have different natural frequencies for passenger cars and race cars. Structural engineers need to calculate the natural frequency of buildings so that the seismic waves produced during earthquakes do not match the natural frequencies of the buildings. This course focuses on the basic theories and concepts, as well as the application of modal analysis in engineering.

Basics of Fluid Dynamics

This course offers an introduction to fluid dynamics. It answers the What Are Fluids? question by examining the physical properties of fluids (versus solids and gases) and defining the many types of fluid flows.

This course provides an overview of fluid statics, a branch of fluid mechanics that looks at fluids at rest for solving pressure problems above and below sea level.

This course covers how fluid kinematics (motion of fluids) is described, and introduces the different coordinate systems used to mathematically calculate fluid flow behavior. Lessons target the rotation, visualization and measurement of fluid motion.

This course looks at the five governing equations of fluid dynamics — conservation of mass (one), momentum (three) and energy (one) — which are commonly referred to as the Navier-Stokes equations. It defines the Reynolds transport and Gauss divergence theorems, as well as the required elements for accurate mathematical modeling.

The focus of this course is on dimensional analysis and similarity. We will first explore the idea and importance of geometric and dynamic similarity. Next, we will identify some important dimensional numbers and use them to non-dimensionalize the Navier-Stokes equations. Finally, we will explore the Buckingham-Pi Theorem, which provides a mathematically formal basis for deriving non-dimensional groups for any physical problem. By using Ansys Fluent to solve simulation examples and homework, you will get hands-on experience and deepen your understanding of the concepts studied in this course.

In this course, you will learn about the basics of viscous laminar flows. These flows can be bounded (internal) or unbounded (external). First, you will learn about the various fluid forces acting on an object in unbounded flows and categorize them as lift and drag forces. Next, you will understand the concept of pressure-driven internal flows as we examine the famous Couette and Poiseuille flows. Finally, we will use Ansys Fluent to simulate some practical engineering flows to gain a deeper understanding of viscous laminar flows.

In this course, you will learn how to obtain analytical solutions to some fundamental problems by making approximations to the fluid flow. You will first study the different types of approximations such as incompressibility, inviscid, etc., and understand their applicability. Then, you will learn in detail about a special class of flows called “potential flows” and explore a whole range of fundamental potential flows. Finally, you will learn about two of the most important flows in theoretical fluid dynamics, which are the flow over a circular cylinder and the flow over a rotating circular cylinder, the latter of which paved the way for understanding and calculating the lift force generated by objects in external flows. To deepen your understanding of all these aspects, there are simulation examples and homework exercises, where you will use Ansys Fluent to simulate the fluid flow problems.

Fundamental Electromagnetics

This Fundamental Electromagnetics Concepts Learning Track was developed by Dr. Kathryn Leigh Smith at the University of North Carolina - Charlotte in partnership with Ansys. It serves as an e-learning resource for the fundamental concepts of electromagnetics. It starts by introducing the basics of vector algebra, which form the foundation of electromagnetic theory. Advanced concepts such as electromagnetics and magnetostatics are introduced subsequently. This learning track is a precursor to more advanced topics that can further your knowledge of electromagnetics.

This course provides an introduction to vector algebra and to the three most common coordinate systems. The four basic functions of vector algebra — addition, subtraction, dot products and cross products — are discussed both graphically and symbolically in each of the three coordinate systems, and the equations for coordinate system transformations are presented. This course was developed by Kathryn Leigh Smith, Asst. Prof. in the Department of Electrical and Computer Engineering at the University of North Carolina-Charlotte in partnership with Ansys.

This course introduces the fundamental properties of electrostatic fields. It defines the concepts of electric field, electric charge and the relationship between them. It also discusses forces between proximate charges, work done by electric fields, field energy storage and electric potential, or voltage. This course was developed by Kathryn Leigh Smith, Asst. Prof. in the Department of Electrical and Computer Engineering at the University of North Carolina-Charlotte in partnership with Ansys.

This course introduces the theory of static magnetic, or magnetostatic, fields. Discussion topics include Biot-Savart’s Law, Ampere’s Law and magnetic potential, which help you to calculate magnetic fields resulting from various current distributions. This course was created for Ansys Innovation Courses by Kathryn Leigh Smith, Assistant Professor, UNC-Charlotte in partnership with Ansys.

In this course, we will discuss several fundamental laws of electrostatics in the context of materials, including the constitutive relation and its ramifications for the free-space equations we developed in the Electrostatics In Free Space course, the boundary conditions for the electric field at a boundary between two dissimilar media, and capacitance. This course was created for Ansys Innovation Courses by Dr. Kathryn Leigh Smith, Assistant Professor, UNC-Charlotte in partnership with Ansys.

In this course, we will discuss several fundamental laws of magnetostatics, in the context of materials. We’ll begin by looking at the constitutive relation between B and H, then move to boundary conditions of the magnetic field at the interface between two media. Then we’ll cover inductance, Magnetic Energy, Forces, and Torques, Faraday’s and Lenz’s Laws, and Motional and Transformer EMF. This overview is part of the Ansys Innovation Course: Magnetostatic Material Interaction. To access this and all of our free, online courses — featuring additional videos, quizzes and handouts — visit Ansys Innovation Courses at www.ansys.com/courses. This course was created for Ansys Innovation Courses by Dr. Kathryn Leigh Smith, Assistant Professor, UNC-Charlotte in partnership with Ansys.

Capturing Complex Response

Every material, when subjected to an arbitrary load, has the potential to change both its volume and its shape. The extent of these changes depends on the nature of the load and the material itself. In this Ansys Innovation Course on “Volumetric and Deviatoric Behavior,” we will present a focused discussion on these components of strain energy and discuss why they constitute an important aspect in many engineering designs. We will introduce formal definitions and mathematical formulations used for quantifying these characteristics. We will also study some practical examples to help reinforce an understanding of the theories and their physical meaning. Upon completion of this course, students should be able to use this information to choose or design the most optimal class of materials based on the volumetric behavior for their application.

The most basic form of constitutive material models in engineering applications are those that represent linear elastic behavior. In this Ansys Innovation Course on “Linear Elastic Materials”, we will introduce the simplified 2D and fully 3D mathematical representation of linear elasticity as governed by Hooke’s law. We will explore three practical examples to help reinforce the theory presented. We will also discuss how directionally dependent behavior influences the theoretical formulation of Hooke’ s Law. While very simple, this study offers practical tips for predicting basic material behavior in many important industrial applications. This course serves as a very important foundation for future studies of more complex material behaviors.

Structures deform not only under loading but also under thermal conditions. Most materials expand with increased temperature. In engineering, this cannot be ignored or it will result in unexpected behavior in the designed structures or products. In some extreme cases, local or global buckling might be triggered because of thermal conditions. Thermal expansion is a material property. Different materials expand to different extents under the same thermal condition. This course defines thermal strain based on the coefficient of thermal expansion. In addition, the relationship between stress and thermal strain is explained with several simulation examples.

Metals have played an important role in the development of technology throughout history. One of the preferred features of metals is their ductility, which is the ability to deform under loads without fracture. Such behavior can no longer be captured by a simple linear stress-strain relationship (linear elasticity). A nonlinear material model, metal plasticity, is developed to better simulate the behavior of metals in engineering. This course will cover the fundamentals of plasticity theory, including the yield surface and the hardening rule. Also, it will provide instructions to define the plasticity model based on experimental data. We will solve several application problems involving metal plasticity.

The study of the mechanical interaction of structures at their surfaces is essential in many applications. An accurate understanding of stress and deformation arising from contact is critical for the design of reliable, efficient and safe products such as disc brakes, gears and tires. Due to its nonlinear nature, contact mechanics is still one of toughest problems in solid mechanics. In this course, we will use the ideas of engineering simulation to study the mechanism of contact problems.

Have you noticed that the sound intensity of a church bell ring decreases with time or that ripples generated in water by throwing a stone vanishes after some time? Why does that happen? Whenever we talk about oscillatory behavior, we hear the term damping. What is damping and what effect does it have on the behavior of an oscillatory structure? Damping is a phenomenon that tries to reduce the oscillatory behavior by dissipating the energy of the oscillation. Damping reduces the bell sound intensity and makes the water ripples vanish. Let’s study damping along with its applications in day to day life. We’ll solve some interesting simulation problems along the way.

Real Viscous Flows

In this course, you will learn about the basics of laminar boundary layer theory. You will explore how to analyze and describe a tiny viscous region that surrounds the body, the boundary layer, and how to estimate the drag acting on the body.

In this course, some fundamental aspects of turbulence will be discussed. The concept of laminar-turbulent transition is first introduced, followed by a detailed discussion on what constitutes turbulence. A theoretical framework, including governing equations, to understand turbulent flows is then presented, followed by a discussion on the closure problem and how to deal with it.

This course provides an overview of internal flows, a branch of fluid mechanics that looks at fluid flows confined by solid walls and their viscous effects. This understanding helps to estimate the losses that an internal passage will develop and enables engineers to design the pumping systems accordingly to sustain the correct flow rate.

This course provides an overview of external flows, a branch of fluid mechanics that looks at situations where an object is moving in a fluid or the fluid is flowing over a stationary object. We will begin by analyzing the forces that are exerted by the fluid on the object. We will then talk about flow separation and free shear flows such as jets wakes and mixing layers. By thoroughly understanding the behavior of external flows, engineers can design fuel efficient aircrafts, automobiles and high speed trains.

In engineering, viscosity is an essential component. But it is not the only one. In this course, we will look “beyond viscosity” and introduce some complex aspects of fluid dynamics which are necessary to understand real-world engineering applications. First, we will discuss fluid compressibility in the lesson “Elements of Compressible Flows.” Next, we will introduce the concept of “Heat Transfer” and learn about the three different modes that facilitate the transfer of heat in engineering. Finally, we will understand and analyze “Flows with Moving and Rotating Objects.”

Heat Transfer in Structures

Heat transfer, or the study of the temperature distribution in structures, plays an important role in almost any engineering system. From small devices such as smartphones to large gas turbines, understanding and controlling heat can improve the performance and reliability of engineered products. This course will provide you a big picture of thermal analysis: why do engineers care about heat transfer problems, where such analysis should be applied and what role should we engineers play in heat transfer simulation. Getting answers to these questions will lay an excellent foundation for you to learn more about heat transfer and apply the knowledge in engineering problems. In addition, the basis of the three heat transfer modes, conduction, convection, and radiation, will be discussed with physical meaning explained and life-related examples.

Heating up a steel bar from one end and holding the other end in hand, you will soon feel the increased temperature. This indicates one of the heat transfer mode, thermal conduction. Thermal conduction transfers heat energy by collision of particles within a body. In engineering, thermal conduction is mathematically described by Fourier’s law. In this course, we will have a comprehensive discussion of Fourier’s law not only for the formulation, but also about its physical meaning. A very important concept, “steady state thermal analysis” is introduced, which assumes stead- state for all thermal loads and boundary conditions without consideration of time. In addition, within the topic of thermal conduction, thermal contact is also introduced to learn how it is handled in simulation.

Thermal capacitance describes the capacity of a material to store heat energy. It is often viewed as the analogy of material mass in transient structural analysis. Transient analysis means analyzing a system in unsteady-state: a state varies with respect to time. A transient thermal analysis solves problems like, how long can the inner side of a steak on grill reach a certain temperature, or, what is the temperature over a hot pot after a certain time. In this course, we will explore how transient thermal analysis is structured with the thermal capacitance term and explain the different parameters related to thermal capacitance. We will also give a discussion on phase change, which is a special process for materials to transform between different phases under the effect of temperature.

If you have an air conditioner in a house, how does the entire space get heated up or cooled down by this machine? The answer is convection. Convection transfers heat within fluids (liquids and gases) through a complex process that combines advection and diffusion. In this course, convection is explained with multiple real-world examples and experiments. For simulation of heat transfer, convection is considered as a boundary condition for a conduction-based solver. The important parameters controlling convection will be covered in this course.

Radiation is one of the three heat transfer modes. Different from conduction and convection, radiation does not require substances as media between the heat source and the heated object. At the molecular level, radiation transforms heat energy by electromagnetic waves. As long as the electromagnetic wave is not blocked, radiation will occur between the objects. To quantify the level of transformation of electromagnetic wave, a parameter called “view factor” is used in heat transfer simulation. In this course, view factor will be discussed in detail for different conditions of surfaces for radiation. For conduction-based solver is the focus, radiation is considered as a nonlinear boundary condition controlled by several parameters. Both the formulation of the radiation and the important parameters controlling radiation will be explained in this course.

Methods of Solving Problems

While most conventional metals undergo plastic deformation at very small to moderate strains, there is a class of non-metallic materials that can exhibit elastic behavior at strains as high as 30% or more, while developing very little or no detectable plastic strain. In this Ansys Innovation Course on “Hyperelasticity”, we will introduce these special materials, their physical characteristics, the laws that capture their behavior, and the challenges associated with calibration. We will discuss formal definitions and mathematical formulations used for quantifying important characteristics unique to these materials. We will also study some practical examples to help reinforce an understanding of the theories and their physical meaning. Upon completion of this course, students should be able to predict the performance of hyperelastic materials in challenging nonlinear applications and make informed engineering decisions to arrive at an optimal design solution.

Structural instability is a phenomenon where a structure deforms a lot while the external force increases by a small amount. In this Ansys Innovation Course on “Structural Instabilities”, we will present a focused discussion on two categories of structural instability: dynamic instability and buckling. We will introduce the cause of these instabilities and their corresponding examples in engineering. We will also study methods of analyzing buckling and approaches to remediate instabilities. Following that, we will reinforce the understanding of these theories and their physical meaning through some practical examples. Upon completion of this course, students should be able to use this information to distinguish structural instabilities and to resolve them by changing design.
Solving a problem and computing to achieve a final product requires many iterations. The more complex the problem, the more iterations are required. In this course, we will focus on how Ansys software solves a simulation problem and the computational resource considerations that go along with doing it efficiently. We’ll deal with a simple problem and a more complex one to show you all the variables you have to take into account for various challenges.
Do you want to capture the frequency response of a system in a limited loading range of frequency but do not want to solve a large, time-consuming dynamic analysis? Mode superposition (MSUP) is computationally less time consuming and finds the response for a given loading by a linear combination/ superimposition of the response of a limited number of mode shapes of the structure. In this course, we will introduce the mode superposition method and see how this concept is used to determine the response of a structure.
In most engineering problems, we want to predict the response of structures to an external loading/excitation, which is the real-life case. There are many examples where we may see resonance or even failure due to external loading acting at a certain frequency. We first discuss the motivation to study harmonic analysis and then proceed with formulation of forced frequency response and applications of the formulation. In this course we demonstrate the use of Ansys to model structures with external excitation along with some challenging problems/quizzes to test your learning.
Time is continuous. Seconds, milliseconds or even microseconds are not the smallest unit of time, because it can be divided into infinite time points. Therefore, in simulation, it’s impossible for us to find a structure’s behavior at every single time point.What we can do is to solve the structure periodically with a designated time interval. How do we find an appropriate time interval and how do we relate the solutions at different time points? The answer is through time integration methods. In this course, we will discuss two main categories of time integration, implicit and explicit. We will learn about their features, differences, applications and how they work for flexible and rigid bodies in simulation.

Compressible Flows

This course introduces the basics of compressible flows. It also discusses the laws of thermodynamics and the one-dimensional equations for gas dynamics. Compressibility and its effects at different speed regimes will be presented.
When a supersonic flow deviates from its flow path because of any reason, such as the presence of solid objects, shock and expansion waves are generated. The focus of this course is on analyzing these compressible supersonic waves. We will first study normal shocks and how to obtain the variation of flow properties across such shocks. Next, we will leverage our understanding of normal shocks and study the physics of flows containing oblique and bow shocks. Finally, we will explore the phenomenon of expansion waves and how these are fundamentally different from shock waves.
By now, we are familiar with the shock-expansion theory. In this course, we will be looking at the applied aspects of this theory. First, we will learn about how shock and expansion waves interact with each other and with their surroundings to generate wave reflections and cancellations. We will then look at certain applications, such as supersonic flows over diamond and curved symmetric airfoils, where we can use the shock-expansion theory to calculate the flow properties which are then used for estimating the lift and drag coefficients. We will then turn our attention to understanding transient phenomena such as finite waves and analyze the famous Sod shock tube problem.
Many critical engineering applications such as jet engines, rocket engines, gas pipelines, wind tunnels, etc., rely on internal compressible flows. While designing these systems engineers try to achieve their goals with minimal losses from compressible waves and friction. In this course we will look into various aspects of internal compressible flows. We will begin with one-dimensional flows with heat addition and friction. Then we will analyze quasi-1D flows and apply the knowledge to the analysis of converging–diverging nozzles, diffusers and wind tunnels. Lastly, we will discuss the method of characteristics and use it in the design of supersonic nozzles.

Pre-loaded Bolted Connections

Bolted connections are part of mechanical assemblies and they are designed to hold the parts together. Designing bolted connections involves understanding the nature of the joint and picking the bolts appropriately. This requires the engineers to understand the mechanics of bolts, different nomenclature standards of bolted fasteners, and various evaluation techniques that are available. In this Ansys Innovation Course on “Overview of Bolted Connections”, we introduce these concepts and educate students on how simulations can be leveraged in designing bolted connections. Upon completion, the students are expected to be familiar with design requirements and the nomenclature of bolted connections.
Evaluation of the structural integrity of assemblies often involves proper modeling and analysis of bolted connections, including the consideration of bolt preload effects. The preload on bolts makes it possible for forces to be transferred between clamped parts effectively, whereas loose bolts may cause failure. Preloaded bolts are also often used in applications with liquids to prevent leakage, so bolt preload is a necessary component of such simulations.
Evaluation of the structural integrity of assemblies often involves proper modeling and analysis of bolted connections, including the consideration of bolt preload effects. The preload on bolts makes it possible for forces to be transferred between clamped parts effectively, whereas loose bolts may cause failure. Preloaded bolts are also often used in applications with liquids and need to prevent leakage, so bolt preload is a necessary component of such simulations.
Evaluation of the structural integrity of assemblies often involves proper modeling and analysis of bolted connections, including the consideration of bolt preload effects. The preload on bolts makes it possible for forces to be transferred between clamped parts effectively, whereas loose bolts may cause failure. Preloaded bolts are also often used in applications with liquids and need to prevent leakage, so bolt preload is a necessary component of such simulations.

Aerodynamics for STEM

How do airplanes fly and stay in the air? How does a streamlined sports car go faster than a bulky truck? This STEM learning track on aerodynamics will let you explore the physics of lift and drag forces. From creating airplane simulations to modeling race cars, Ansys simulation technology is used worldwide to understand lift and drag and create very cool products.
How do airplanes fly and stay in air? The Wright Brothers figured this out by mastering a physics force called “lift”. Mostly created by the wings, lift holds an aircraft in the air. This fun and engaging course will teach you more about this topic.
How does a streamlined sports car go faster than a bulky truck? This is due to a physics phenomenon called “drag” or “drag force” where air particles push against the front of objects, slowing them down. This fun and engaging course will teach you about the basics of aerodynamics and how airplanes stay up in the air.

Heat Transfer in Fluids

From HVAC systems to electronics cooling, from power generation to food preparation, heat transfer is everywhere. In fact, the very existence of life on Earth depends on the heat from sun. The process of heat transfer occurs between two systems that are at different temperatures, with the system at higher temperature transmitting energy to the system at lower temperature. This transmission of energy can take place via three modes: conduction, convection and radiation. Often, in real-world situations, heat is transferred by all the three modes simultaneously. In this course, we will start by discussing some fundamental concepts of thermodynamics, understand the different modes of heat transfer and finally dig deeper into the process of heat transfer through conduction.
Forced convection heat transfer refers to a process in which fluid flow generated by external means, such as a fan or an externally imposed pressure gradient, extracts or imparts heat from or to objects at temperatures different from the flow temperatures. Forced convection is commonly used in applications such as cooling of electronic components by fans, heating of homes using forced air blowers, cooling of oil and coolants in vehicles using externally forced air, etc. In this course, we will first look at some fundamental aspects of forced convection and then go on to discuss the finer details regarding the velocity and thermal boundary layers. Finally, we will analyze the forced convection heat transfer in certain external flows such as flow over a flat plate, cross-flow over a cylinder, cross-flow over a tube bank, and impinging jet flow.
Forced convection is a critical phenomenon in many engineering applications involving heat and mass transfer. The fluids are forced to flow through pipes and ducts to accomplish the desired transfer of thermal energy. For such applications the friction at the walls creates the pressure drop across the flow and the thermal convection governs the overall heat transfer. In this course, we will start with the analysis of velocity and thermal fields in internal flows. We will then investigate general heat transfer analysis in internal flows and discuss various laminar and turbulent pipe flow correlations. Lastly, we will introduce different types of heat exchangers and learn how to do design and performance analysis.
Have you ever wondered how a cup of hot coffee cools down when you leave it on a table? Even though there is no external forcing, convection heat transfer still occurs due to the convection currents that exist within the ambient air owing to density gradients. This is referred to as natural convection and is the focus of this course. Natural convection plays an important role in many industrial applications such as power generation, HVAC systems and electronics cooling. Moreover, it is the driving force for many natural processes such as ocean and atmospheric currents. In this course, we will start with understanding the physics behind natural convection in greater detail and follow it up with a discussion of the boundary layer profiles in natural convection. We will then discuss how natural convection varies in external and internal flows by analyzing several canonical cases such as the flow over a plate, the flow between parallel plates, flows insides enclosures, etc.

Cornell SimCafe Fluids

This SimCafe Fluids Learning Track was developed by Dr. Rajesh Bhaskaran at Cornell University in partnership with Ansys. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. The following courses show how to solve selected fluid flow problems using Ansys Fluent. These tutorial-based courses follow the same high-level steps; starting with pre-analysis and ending with verification and validation. The successful completion of these simulation courses will provide a thorough understanding of how to set up a CFD simulation using Ansys Fluent.

Bio-medical researchers have been relying on computational fluid dynamics to model and understand the physical mechanisms behind the formation and progression of hemodynamic disorders. Wall shear stress (WSS) exerted on the walls of the blood vessel due to the flow of blood is one of the main pathogenic factors leading to the development of such disorders. The magnitude and distribution of the WSS in a blood vessel can provide an insight into the locations of possible aneurysm growth. Moreover, blockages that build up over time can be predicted by having a qualitative understanding of the flow profile. Computational Fluid Dynamics can be used for modeling and understanding such vital internal flows and insights gained from such studies can help design patient-specific treatments. In this Ansys Fluent tutorial, you will learn how to model three dimensional internal blood flow in a bifurcating artery. You will create the computational mesh and set up the boundary conditions needed for the simulation. The Non-Newtonian behavior of blood flow will be modeled using the Carreau model. Moreover, a realistic time-varying boundary condition will be implemented using User Defined Functions (UDF) in order to mimic the pulsatile nature of blood flow. This SimCafe Fluids Course was developed by Dr. Rajesh Bhaskaran at Cornell University in partnership with Ansys. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. The fundamental concepts and the steps needed to successfully model this fluid flow problem are explained using immersive step-by-step walk-through videos.

One of the most common application of a converging-diverging nozzle is in a supersonic wind tunnel. The inlet flow into the converging section is subsonic and as the cross sectional area of the converging section decreases, the flow velocity increases until it reaches sonic condition at the throat. In the diverging section of the nozzle, the flow is accelerated further such that the flow velocity at the nozzle exit is the required Mach Number at the test section. Another critical application of converging-diverging nozzle is in the area of propulsion, where it is designed to generate the required thrust and assist in the maneuverability of the aircraft or rocket. In this regard, it is important to analyze the flow within the nozzle and reduce the total pressure losses. In this tutorial, you will learn how to setup the simulation to analyze the flow through the nozzle by creating the geometry of the nozzle, meshing the geometry and setting up the physics and numerical model. This SimCafe Fluids Course was developed by Dr. Rajesh Bhaskaran at Cornell University in partnership with Ansys. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom.

Airplane wings have streamlined cross-sections. When air flows over these wings, the aerodynamic forces generated on the wing maintains the aircraft in the air. The vertical force responsible for keeping the aircraft in flight is called the lift force. In aerodynamics, the relative velocity of the aircraft and its surrounding fluid (air) is typically compared with the speed of sound using a dimensionless number – the Mach Number. The larger the Mach number, the faster is the speed of the aircraft. For most commercial inter-continental flights, the typical Mach number at the cruising altitude is between 0.6 and 0.8. This flow regime is called Subsonic regime. When the Mach number is between 0.9 and 1.2, the flow regime is commonly referred to as Transonic flow. When the Mach number is greater than 1, the flow is typically Supersonic. This SimCafe Fluids Course was developed by Dr. Rajesh Bhaskaran at Cornell University in partnership with Ansys. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. In this tutorial, we will learn to model the transonic flow over a 3D wing by following the end-to-end workflow in Ansys Workbench.

Cooling electronics components is important for smooth, reliable operation. The thermal power generated by the electronics is detrimental to their operation and often leads to premature failure and a shortened lifecycle. The thermal energy generated by these semiconductor devices must be transported away from the electronics to maintain the temperature of the electronics below a specified critical value for reliable operation. Any temperature higher than the critical temperature can damage the electronics.  This is true for laptops, desktops and even smartphones. In most cases, engineers designing these thermal solutions rely on convective heat transfer for transporting the thermal power away from the electronics. These thermal solutions often involve blowing relatively cooler air over electronics. The thermal power from the electronics is convected by this cooler air, causing a rise in the fluid temperature. This SimCafe course was developed by Rajesh Bhaskaran, Swanson Director of Engineering Simulation at Cornell University in partnership with Ansys. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. In this tutorial, we will learn to model the convective heat transfer through an electronics box by following the end-to-end workflow in Ansys Workbench.

Diffusion is a process resulting from the movement of a substance from an area of high concentration to an area of low concentration. It is completely driven by a concentration gradient. A gas held in a container is a good example of diffusion. These fluid particles are continuously colliding with each other and with the walls of the container. Eventually, these gas particles spread to occupy the entire volume of the container in which they are held. Diffusion occurs on its own and does not require any external stirring, or shaking. The smell of incense sticks or diffusers filling up a room full of still air is a good example of diffusion. Another example is heat conduction in solids and fluids which involves thermal energy transported, or diffused, from higher to lower temperatures. This SimCafe course was developed by Rajesh Bhaskaran, Swanson Director of Engineering Simulation at Cornell University and Keith Alexander Works, in partnership with Ansys. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. In this tutorial, we will learn to model a three-dimensional diffusion problem in Ansys Fluent and compare the obtained numerical solution with the analytical result.

Combustion includes two processes — thermal and chemical — in which a hydrocarbon fuel reacts with an oxidant to form products, accompanied by the release of energy in the form of heat. It is an integral part of various engineering applications like internal combustion engines, aircraft engines, rocket engines, furnaces, and power station combustors.Combustion simulation is used broadly during the design, analysis, and performance stages of the above-mentioned applications. This SimCafe Fluids Course was developed by Dr. Rajesh Bhaskaran, Swanson Director of Engineering Simulation at Cornell University in partnership with Ansys. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. In this tutorial, we will learn to model partially premixed combustion by following the end-to-end workflow in Ansys Workbench.

Multi-phase flows is simply any fluid flow system consisting of two or more distinct phases flowing simultaneously in a mixture with some level of phase separation at a scale well above the molecular level. A mixing layer is formed when two parallel streams of fluids are moving at different velocities such that the velocity at the fluid-fluid interface is non-zero. In the absence of dissipative forces such as viscosity, small perturbations at the fluid–fluid interface lead to the creation of vortices at the interface.For a particle-laden flow at this interface, these vortices will affect the flow of particles based on the particle mass. A particle-laden flow is a multiphase flow where one phase is the fluid and the other is dispersed particles. Governing equations for both phases are implemented in Ansys Fluent. This SimCafe Fluids Course was developed by Dr. Rajesh Bhaskaran, Swanson Director of Engineering Simulation at Cornell University and Chiyu Jiang in partnership with Ansys, and was last modified by Alumni Chiyu Jiang. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. In this tutorial, we will learn to model the 2D periodic double shear layer by following the end-to-end workflow in Ansys Workbench.

Most fluid flows (gas or liquid) are turbulent in nature.These flows are characterized by unsteady and irregular fluctuations of transport quantities such as mass, momentum and species in both space and time. These fluctuations enhance flow mixing. Examples of these flows are widespread — from ocean waves and cyclones to airflow over an automobile, from jet engine exhaust to flow inside gas pipelines. Generally, there are two types of turbulent flow structures (or eddies) — large and small scale. Turbulence modeling attempts to capture these eddies to understand the overall flow field.

This SimCafe Fluids Course was developed by Dr. Rajesh Bhaskaran, Swanson Director of Engineering Simulation at Cornell University in partnership with Ansys, and was last modified by Sebastien Lachance-Barrett. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. In this tutorial, we will learn to model turbulent flow inside a pipe using the Large Eddy Simulation (LES) by following the end-to-end workflow in Ansys Workbench.

Cornell SimCafe Structures

This SimCafe Structures course was developed by Dr. Rajesh Bhaskaran at Cornell University in partnership with Ansys. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and to provide a resource for supplementary learning outside the classroom. This learning track consists of a set of learning modules focused on using Ansys simulations to solve problems in solid mechanics. The learning modules lead you through the steps involved in solving a selected set of problems using Ansys solutions. This learning track not only provides the solution steps but also the rationale behind them. It is worthwhile for you to understand the underlying concepts as you go through the learning modules in order to be able to correctly apply Ansys solutions to other problems.

This SimCafe Structural Course was developed by Dr. Rajesh Bhaskaran at Cornell University in partnership with Ansys. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. The purpose of this course is to showcase, in a relatively simple situation, where simple beam theory is no longer as valid as it is in the limit of a long and slender beam geometry.  In some commercial codes, simple one-dimensional cubic beam elements for bending deflection, do not capture shear deflection when the beam is no longer slender. Alternatively in Ansys, if shear deflection is accounted for in the 1D element formulation, results for the beam’s tip deflection will not agree with tip deflections predicted by simple Euler-Bernoulli beam theory. This course is meant to highlight where it is relatively straightforward to apply 3D FEA and resolve a correct solution.

This SimCafe Structural Course was developed by Dr. Rajesh Bhaskaran at Cornell University in partnership with Ansys. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. The following course shows how to solve Cardiovascular Stent Simulation using Ansys Structural. Coronary Artery Disease kills nearly 1 in 4 Americans every year. Implantable stent treatments for arterial disease are constantly evolving with implantable stent innovations leading the way. Over 600,000 cardiovascular stents are implanted every year just in the United States alone. Stents may look relatively simple but are highly engineered lifesaving medical devices. It involves advanced material modeling, complex interaction with the arteries, and extremely high demand for accuracy. Apart from conducting experiments on stents, FEA is a tool that engineers and researchers use extensively to study and design stents. It has the ability to identify some mechanical characteristics of coronary artery stents that may not be easily obtained using traditional mechanical testing. We will go step by step to set up and run a Balloon-Expandable stent simulation.   

This SimCafe Structural Course was developed by Dr. Rajesh Bhaskaran at Cornell University in partnership with Ansys. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. The following course shows how to solve a Rat Femur Bending Simulation using Ansys Structural. A femur is the upper bone of the leg. In biomedical engineering, the mechanical properties of the femur can be studied through conducting tests on rat femur.  The valuable data from tests can then be applied in simulation to predict behaviors of other femurs.  We will show you step by step how to conduct a bending simulation on a rat femur and evaluate the results.

Stepped shafts are widely used in drive trains.They are generally holding large gears and cams, which are key elements in power transfer. Mostly supported by bearings at the end, the shaft experiences bending loads, axial thrust and torsional loads. The shaft must have greater strength to withstand these loads.A factor of safety is used to design the shaft so that higher loads limits are assumed than the working load limit. With gears and cams engaged with other parts in the assembly, any deviation in the shaft’s shape can cause a catastrophic effect.The assembly could fail long before the shaft reaches its failure limit and, therefore, the study of the shaft is extremely important. This SimCafe course was developed by Rajesh Bhaskaran, Swanson Director of Engineering Simulation at Cornell University in partnership with Ansys; it was last modified by Sebastien Lachance-Barrett. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. The following course shows how to estimate the axial stress concentration on a stepped shaft under axial tension using Ansys Structural.

Four-point bending strength is performed to analyze the flexural strength of a material. This test is useful for materials that tend to crack (brittle failure) under the bending load (like composites, concrete beams, and car axles). A common example of such a material is the electronic PCB. The four-point bending test is conducted on these PCBs to determine their material strength.
This SimCafe course was developed by Rajesh Bhaskaran, Swanson Director of Engineering Simulation at Cornell University in partnership with Ansys; it was last modified by Sebastien Lachance-Barrett. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. In this tutorial, we will learn to conduct this test, virtually, on a simple T-beam made of structural steel, to understand the boundary condition setup by following the end-to-end workflow in Ansys Structural.

Pressure vessels are used in transportation for storage of gases and liquids. The pressure inside is multiple times higher than the pressure outside, so they are called “pressure vessels”. Spherical shapes are ideal for pressure vessels since they have a uniform stress distribution in all directions. Rectangular or polygonal shapes can have a very high stress concentration in corners, which can result in weakness or premature wear and tear of the vessel. The most practical pressure vessels are cylindrical with welded elliptical ends. Many gases are stored at very high pressure in the liquid form. Pressure vessels are subjected to catastrophic failure, explosions due to temperature/pressure rise, or crack formations in the vessel metal. The pressure vessels are designed mainly to have high strength in both the circumferential (hoop strength) and axial directions. Also, a factor of safety ensures that the vessel is designed for higher loads than the actual working loads.

This SimCafe Structural Course was developed by Dr. Rajesh Bhaskaran, Swanson Director of Engineering Simulation at Cornell University in partnership with Ansys. It was last modified by Sebastien Lachnace-Barrett. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. The following course shows how to estimate the hoop, axial, and radial stresses in pressure vessels using Ansys Structural.

This course demonstrates the structural analysis of a telescope truss model.The design of the telescope truss should be able to sustain dynamic loads and must be flexible enough to provide support for different motions. It has to withstand varying loads due to gravity, temperature, winds, etc. The installation, maintenance and durability are major challenges in the design of the telescope truss. FEA simulation helps to predict the behavior under these real-life physical conditions. This SimCafe Structural Course was developed by Dr. Rajesh Bhaskaran, Swanson Director of Engineering Simulation at Cornell University in partnership with Ansys, and was last modified by Sebastien Lachanc-Barrett. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. In this tutorial, we will learn an end-to-end workflow for importing a realistic geometry and understand the importance of FEA simulations when designing the telescope truss.

Buckling analysis is important as buckling happens suddenly which can create catastrophic failure. Buckling analysis calculates the buckling load factor and associated mode shapes. The buckling load factor multiplied by the applied load gives the magnitude of the compressive load that can cause buckling.Mainly slender, thin-walled columns should undergo buckling analysis as they are the most susceptible to this mode of failure.This SimCafe Structural Course was developed by Dr. Rajesh Bhaskaran, Swanson Director of Engineering Simulation at Cornell University in partnership with Ansys, and was last modified by Sebastien Lachance-Barrett. It serves as an e-learning resource to integrate industry-standard simulation tools into courses and provides a resource for supplementary learning outside the classroom. In this tutorial, we will learn to analyze buckling on a simple column, to understand the boundary condition setup and results interpretation by following the end-to-end workflow in Ansys Structural.

Ansys Lumerical FDE

In this learning track we will start with the discussion of the algorithm used to find the eigenmodes of a given structure and the properties of those modes in Ansys Lumerical FDE. We will then learn about the material database and how to add new materials followed by a detailed discussion of the properties that are set in the Ansys Lumerical FDE solver. Next, we will learn about the workflow for setting up an FDE simulation to find the supported modes of a waveguide and analyze the frequency response of the modes. We will also learn what types of devices and applications can be simulated using the FDE solver, and the types of results that can be obtained using the analysis tools. Finally we will discuss how to run the Ansys Lumerical FDE solver, use the built-in analysis options, get results using the scripting language, and export results. We will also discuss convergence testing for verifying result accuracy.

In this course, we will demonstrate the workflow for setting up an Ansys Lumerical FDE simulation to find the supported modes of a waveguide and analyze the frequency response of the modes. We will learn what types of devices and applications can be simulated using the FDE solver, and the types of results that can be obtained using the analysis tools.

In this course, we will discuss the algorithm used to find the eigenmodes of a given structure and the properties of those modes in Ansys Lumerical FDE. We will also explain the overlap and power coupling calculations, the feature that tracks modes as a function of frequency, and how properties such as dispersion and group velocity are calculated. By the end of this course, you will be able to describe the algorithm used by the FDE solver, know when the FDE method can be applied, understand the difference between the overlap and power coupling quantities, and know how the overlap frequency sweep calculations are performed.

In this course, we will learn about the material database and how to add new materials. We will also learn when broadband material fits need to be generated and how to check material fits. By the end of this course, you will be able to add new materials to the material database, know when broadband material fits need to be used, check material fits in the material explorer, and know where to find more information on the material models/

In this course, we will learn about the properties that are set in the Ansys Lumerical FDE solver region and mesh override regions. The FDE solver region is where the solver region geometry, mesh and boundary conditions can be set.

In this course, we will learn how to run the Ansys Lumerical FDE solver, use the built-in analysis options, get results using the scripting language, and export results. We will also discuss convergence testing for verifying result accuracy. By the end of this course, you will be able to understand the difference between layout and analysis modes, calculate modes of straight and bent waveguides using the FDE solver, know how to use the data analysis group, understand the difference between the integrated frequency sweep tool and the general parameter sweep tool, plot and export results, explain what convergence testing is and why it is necessary, and know where to find information about script commands used for FDE analysis.

Ansys Lumerical EME

In this learning track, we will first discuss the basic workflow for EME (Eigenmode Expansion) simulations, and when you should use EME simulations. Then we will cover some background on the calculations performed for the Eigenmode Expansion (EME) method used for Ansys Lumerical EME simulations. Floowing this, we will cover the basic settings of the Ansys Lumerical EME solver region, including the simulation region geometry, cell definition, periodicity and boundary conditions. We will then discuss ports, cells, and monitors. We will also learn how to interpret the results obtained by running Ansys Lumerical EME simulations. Finally, we will discuss the sources of error in an Ansys Lumerical EME simulation and how to verify the accuracy of simulation results by using convergence testing and error diagnostics.

In this course, we will cover the basic workflow for EME simulations, and when you should use EME simulations. We will also go through a hands-on step-by-step example showing how to set up, run and analyze results for a spot size converter.

This course will cover some background on the calculations performed for the Eigenmode Expansion (EME) method used for Ansys Lumerical EME simulations. The EME method makes use of the Finite Difference Eigenmode (FDE) solving algorithm, which is covered in detail in the FDE learning track. The FDE learning track is a recommended prerequisite for this course, so the FDE algorithm will not be discussed in detail here.

This course will cover the basic settings of the Ansys Lumerical EME solver region, including the simulation region geometry, cell definition, periodicity and boundary conditions. Note that many of the settings are shared with the FDE solver settings. Those settings will not be covered here. See the Lumerical FDE Learning Track for more information.

In this course, we will discuss ports, cells, and monitors. It will cover how to add and set up ports, and select port modes. This will be followed by a discussion of monitor types and how to set them up.

In this course, we will look at the results after running Ansys Lumerical EME simulations and discuss how to interpret those results. Examples demonstrating how to use the periodicity settings and the propagation sweep tool will also be presented.

In this course, we will discuss the sources of error in an Ansys Lumerical EME simulation and how to verify the accuracy of simulation results by using convergence testing and error diagnostics.

Ansys Lumerical varFDTD

In this learning track, we will first learn how to set up and run an Ansys Lumerical varFDTD simulation of a double bus ring resonator, collect the results and discuss how the results compare to 3D FDTD simulation results. We will then discuss the effective index method used by the Ansys Lumerical varFDTD solver to collapse a 3D geometry into a 2D simulation and highlight some of the differences between varFDTD and a traditional FDTD simulation. Following this, we will discuss the solver region, materials, sources and monitors used in varFDTD. Finally, we will show several example devices and results that can be obtained from the varFDTD solver.

In this course, we will briefly explain what Ansys Lumerical varFDTD is and how it works. We will introduce some key example devices where the varFDTD solver can be used.

In this course, we will demonstrate how to set up and run an Ansys Lumerical varFDTD simulation of a double bus ring resonator, collect the results and discuss how the results compare to 3D FDTD simulation results.

In this course, we will discuss the effective index method used by the Ansys Lumerical varFDTD solver to collapse a 3D geometry into a 2D simulation. The course starts by describing the simulation workflow, which highlights some of the differences between varFDTD and a traditional FDTD simulation. After the workflow is introduced, more information will be provided on the algorithm used to compress the simulation into an effective 2D simulation.

In this course, we will discuss the solver region, materials, sources and monitors used in varFDTD. Most of the features are similar to those in FDTD, so we will only focus on the aspects of the features that are unique to varFDTD.

The Ansys Lumerical varFDTD solver can be used to simulate a range of planar integrated optics components. In this course, we will show several example devices and results that can be obtained from the varFDTD solver.